[o_nate]

I think its easy for us to think we can understand what a program is going to do when we're dealing with high level abstractions. I think if we really came to grips with everything the program is doing all the way down to the hardware level, we might have less confidence that we can predict what its going to do with 100% accuracy every time, even in the case of supposedly simple programs.

[drdeca]

Well, of course at the real hardware level there will be some non-zero amount of nondeterminism, but the error correction steps that have been implemented are enough to make the probability of it behaving contrary to the design of the hardware, low enough to be pretty negligible.

And if you want additional assurance (due to, e.g. the computation being very long) you could probably use some cryptographic techniques to produce a certificate that the output is as it should be, and you can check that certificate as many times as you want to avoid possible random hardware errors in the process of checking the certificate.